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# Let X ~ Geom(p), let n be a non-negative integer, and let ISBN: 9780073401331 38

## Solution for problem 17E Chapter 4.4

Statistics for Engineers and Scientists | 4th Edition

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Problem 17E Problem 17E

Let X ~ Geom(p), let n be a non-negative integer, and let Y ~ Bin(n, p). Show that P(X = n) = (l/n)(1/n)p(Y=1).

Step-by-Step Solution:

Solution :

Step 1 of 1:

Given and Where mean and variance .

Here non-negative integer is n.

Our goal is :

We need to prove that P(X=n)= .

Now we have to prove that P(X=n)= .

P(X=n)= The formula of the geometric distribution is

P(X=n)= Where q = (1-p)

So P(X=n)= Then,

P(X=n)=  The formula of the binomial distribution is   Here the probability of X is n and the probability of Y is 1.

P(X=n)=  Here and = p.

P(X=n)=  Therefore P(X=n)= .

Step 2 of 1

##### ISBN: 9780073401331

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Let X ~ Geom(p), let n be a non-negative integer, and let